Minimum Time Bilateral Observer Design for 2 x 2 Linear Hyperbolic Systems

Abstract

In this paper we derive a minimum time convergent bilateral observer for a 2×2 system of linear coupled first-order 1-D hyperbolic PDEs. First, a Volterra integral transformation is combined with a Fredholm integral transformation to derive a minimum time collocated observer for a class of 2+2 systems (four coupled PDEs). Then, it is shown that the 2 ×2 system (two coupled PDEs) can be transformed to a 2+2 system via an invertible coordinate transformation. The 2×2 bilateral observer is subsequently obtained from the 2+2 minimum time collocated observer, and it is shown that it has convergence time equal to the theoretical minimum time for bilateral sensing. The performance of the 2×2 bilateral observer is demonstrated in a simulation and compared to a previously derived observer using only unilateral sensing.